Representing Quadratic Surd on the Number Line

Q. Represent $\sqrt{5}$ on a number line with a given length of $\sqrt{2}$ and $\sqrt{3}.$
Consider the following steps and arrange them in a proper sequence.

(a)	Connect the other endpoints of both the lines to draw the hypotenuse.
(b)	Draw a perpendicular line of length $\sqrt{3}$ on the number line from the right end of the line of length $\sqrt{2}.$
(c)	Measure the length of the hypotenuse using a compass and mark it on the number line to represent $\sqrt{5}.$
(d)	Draw a line of length $\sqrt{2}$ on a number line with its left end on 0.

1. $a\to b\to c\to d$
2. $d\to b\to a\to c$
3. $a\to b\to d\to c$

Q. Report the approximate value of $\sqrt{3}$ with the help of the attached figure below

1. 1.7

Q. To represent $\sqrt{6}$ on a number line, which of the following base and perpendicular lengths can help?

1. $\sqrt{3}\&\sqrt{3}$
2. $\sqrt{2}\&2$
3. $1\&\sqrt{5}$

Q. Comment on the given statements:
Statement I: $\sqrt{12}$ cannot be precisely represented on a number line.
Statement I: $\sqrt{12}$ is a non-terminating and non-repeating decimal number.

1. Both statement I and statement II are correct, and statement II is a correct reason of statement I
2. Statement II is correct, but statement I is wrong.
3. Both the statements are wrong.

Q. Which of the foolowing steps are required to represent $\sqrt{10}$ on a number line.

1. Draw a line of length 3 units from 0 in right direction on a number line.
2. Draw a perpendicular line of length 1 unit from right end of the line of length 3 units.
3. Draw a horizontal line of length 1 unit from right end of the line of length 3 units.
4. Connect the other end points of both lines to draw the hypotenuse.
5. Measure the length of the hypotenuse using a compass and mark it on the number line to represent $\sqrt{10}.$